MODELLING OF STRESS-STRAIN STATE OF SAMPLES WITH OCTAGONAL STRUCTURE MANUFACTURED BY 3D-PRINTING TECHNOLOGY.

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Justification

Research in the field of designing materials with specified properties for transport and technological machines has shown that a change in the geometric configuration of the internal structure significantly affects the ability of a metamaterial to exhibit new properties not peculiar to its initial state [1-4]. One of the illustrative examples in this field is the development of metamaterials with a negative refractive index of light, the properties of which are realized solely by changing its structural geometry. Recently, advances in 3D printing technologies have facilitated the development and manufacture of new types of materials, making processes more accessible and economical for various technological applications, including in the development and production of high-tech machinery and equipment used in agriculture [5]. A promising area of research is also the development of elastic three-dimensional structures of metamaterials [6].

The technology of 3D printing by the FDM method is currently widespread and consists in melting the plastic filament inside the printer nozzle, squeezing it onto the assembly platform, creating a part layer by layer [7]. Increasing the availability of 3D printers allows for extensive research in the field of materials aimed at creating parts with improved functionality due to geometric modifications of their design [8]. The advantage of intelligent design of the geometric structure of the product material is also the ability to provide its new functionality. For example, by intentionally increasing the plasticity of the material, its properties can be used to increase the elasticity of the part [9].

In this study, stress-strain states of metamaterials with various geometric configurations were studied, which can be manufactured using 3D printing technology and used to replace standard materials of parts of agricultural machinery and equipment [10]. A series of numerical experiments was carried out using a computer-aided design and engineering analysis system.

Goal

The main purpose of the study was to analyze the influence of the geometric configuration of metamaterials on their mechanical properties in order to develop materials for agricultural machinery parts that provide increased strength and resistance to deformation.

Methods

This article discusses the structures of materials consisting of regular and irregular octagons (Figure 1). These structures have a definite advantage over other geometric shapes of metamaterial cells due to their ability to create a mosaic structure without gaps. Elements of various thicknesses (0.25, 0.5, 0.75 and 1 mm) were used to form the spatial structure of the metamaterial. The thickness of the cells was selected in such a way as to match the sizes of common nozzles for 3D printers based on FDM technology (from 0.25 mm to 1 mm), to ensure the possibility of manufacturing samples of metamaterials with the structure in question and further conducting field experiments.

The dimensions of the cells were selected in such a way that they occupied an area of 40x40 mm. To create 4x4, 5x5, 8x8 and 10x10 grids on a 40x40 mm surface, four basic sizes were selected that are applicable to both types of the studied elementary cells.

The main purpose of this study is to study how irregular shapes of elementary octagonal cells affect the mechanical properties of metamaterials under different loading conditions compared to regular shapes.

The use of cells with the shape of regular octagons in the structure of the material does not allow to completely cover a given area and leads to the formation of small squares. On the contrary, the advantage of cells with the shape of irregular octagons is the complete coverage of a given area without the formation of small geometric elements at the joints of the cells.

Simulation models were performed using the SolidWorks Simulation computer-aided design and engineering analysis system. The same boundary conditions were applied in all models. A uniform load of 10 N was applied to each model, while deformations were recorded. The linear behavior of the material was assumed as an assumption for low loads and deformations. Stress calculations were performed according to the von Mises plasticity condition.

These assumptions and conditions provided a standardized approach to modeling and analyzing the behavior of models of material structures under specified loads.

The modeling process consisted of the following steps:

64 simulation models were developed with different parameters of their structure (cell shape, size and thickness varied). The material used for 3D printing is acrylonitrile butadiene styrene (ABS), the mechanical properties of which are shown in Table 1.
For each simulation model, the parameters of a flat two-dimensional standard grid with element sizes from 0.02 to 0.7 mm were set.
Numerical simulation of static loading was performed for each simulation model (Figure 3) and the results were obtained, which were then analyzed.

The metamaterial model is a 40x40 mm square consisting of base cells shaped like regular and irregular octagons. The metamaterial model is located between two parallel plates made of absolutely rigid material, one of which is a support ("fixed geometry"), and a compressive load is applied to the second in the normal direction (Figure 2).

Results

The obtained data on stresses, displacements and deformations under a given load for each model were analyzed. According to the results of the research, the maximum stresses observed in each case did not exceed the tensile strength of the specified ABS material.

A visual representation of the simulation results of various metamaterial structures is shown in Figure 3 (Figure 3a is a structure model consisting of cells with the shape of a regular octagon, compressed in the longitudinal direction, Figure 3b is a structure model consisting of cells with the shape of a regular octagon, compressed in the transverse direction, Figure 3c is a structure model consisting of cells with the shape of an irregular octagon, compressed longitudinally, 3d drawing – a model of a structure consisting of cells with the shape of an irregular octagon, compressed in the transverse direction).

Discussion

The displacement analysis revealed the greatest deformations in the study of the structure with the base cells having the smallest wall thickness (0.25 mm), which emphasizes the significant influence of the wall thickness of the cell on the mechanical properties of the metamaterial.

Graphs of the dependence of the displacement coefficients on the thickness of the cell wall for various sizes and shapes of the cells under study were obtained. As an example, Figure 4 shows such a graph for a model of the metamaterial structure consisting of cells with the shape of a regular octagon, compressed longitudinally. As the thickness and number of base cells increased, the differences in displacement coefficients approached one. This feature allows you to accurately set such mechanical properties of the metamaterial as stiffness and strength, which allows you to create metamaterials taking into account the specifics of their operation.

unchanged.

Conclusion

The results of the study emphasize the role of the internal structure in determining the mechanical properties of a metamaterial and can be used in designing the structure of metamaterials for promising machine parts and equipment. Future research will be devoted to the study of the structural features of metamaterials and their practical application to improve the designs of parts of agricultural machinery and equipment.

Additional information
THE CONTRIBUTION OF THE AUTHORS. All authors confirm that their authorship meets the international ICMJE criteria (all authors have made a significant contribution to the development of the concept, research and preparation of the article).
CONFLICT OF INTEREST. The authors declare the absence of obvious and potential conflicts of interest related to the publication of this article.
THE SOURCE OF FINANCING. This article was prepared as part of the 1st stage of research work carried out at the expense of the federal budget (the source of funding is the Ministry of Education and Science of the Russian Federation) on the topic: "Development of scientific, methodological and practical foundations of reverse engineering for solving complex import substitution problems in the agro-industrial complex of the Russian Federation" (code of the scientific topic FZNW-2024-0026).

Table 1 Mechanical characteristics of the simulated material

Table 1 Mechanical characteristics of the modelled material

No. p / p

    

Characteristic

    

Meaning

 

1

    

Material

    

ABS plastic

 

2

    

Yield strength, Mpa

    

30

 

3

    

Tensile strength, Mpa

    

40

 

4

    

Modulus of elasticity, Mpa

    

2000

 

5

    

Poisson's ratio

    

0,3

 

6

    

Mass density, kg/m3

    

1020

Fig. 1. The studied metamaterials: a) the structure; b) the shape of the cell

Fig. 2. Various types of models for simulation

Fig. 3. Modeling of static loading of the studied structures of metamaterials compressed in the longitudinal and transverse directions: a) and b) with cells of the shape of a regular octagon; c) and e) with cells of the shape of an irregular octagon

About the authors

Ilya Sergeevich Nefelov

State University of Management

Email: iljanefelov@yandex.ru
SPIN-code: 6972-3967

Ph.D., Researcher at the Laboratory of Reverse Engineering

Russian Federation, 99 Ryazansky Prospekt, Moscow, 109542

Vladimir Viktorovich Filatov

State University of Management

Author for correspondence.
Email: 2vfilatov@gmail.com
SPIN-code: 2897-2925

Ph.D., Leading Researcher at the Laboratory of Reverse Engineering

Russian Federation, 99 Ryazansky Prospekt, Moscow, 109542

Dmitry Yuryevich Malakhov

State University of Management

Email: malahow_dm@mail.ru
SPIN-code: 3578-5244

Ph.D., Researcher at the Laboratory of Reverse Engineering

Russian Federation, 99 Ryazansky Prospekt, Moscow, 109542

References

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